Question

An investigation of the ability of a hybrid tomato plant to produce a certain protein found that the amount x of the protein produced in the plant had a mean of

113.1113.1

micrograms per gram of fresh weight with a standard deviation of

8.28.2.

Consider a random sample of

n equals 65n=65

hybrid tomato plants and let

x overbarx

represent the sample mean amount of the protein produced. Would it be expected to observe a value of

x overbarx

less than

112112

micrograms per gram of fresh weight? Explain. Consider an event with a probability less than 0.05 unlikely.

Select the correct choice below and fill in the answer box within your choice.

(Round to four decimal places as needed.)

A.It would

bebe

expected to observe a value of

x overbarx

less than

112112

micrograms per gram of fresh weight because the probability of such an event is

nothing

which

isis

unlikely.

B.It would

bebe

expected to observe a value of

x overbarx

less than

112112

micrograms per gram of fresh weight because the probability of such an event is

nothing

which

is notis not

unlikely.

C.It would

not benot be

expected to observe a value of

x overbarx

less than

112112

micrograms per gram of fresh weight because the probability of such an event is

0.14920.1492

which

isis

unlikely.

D.It would

not benot be

expected to observe a value of

x overbarx

less than

112112

micrograms per gram of fresh weight because the probability of such an event is

0.14920.1492

which

is notis not

unlikely.

Answer 1

it is given that

population mean

population standard deviation

we have to find

using the formula

using z distribution, check 1.0 in first left column and 0.08 in first row, then select the intersecting cell

we get

Since the probability is above 0.05, so this event is likely.

Thus, we can say that it would be expected to observe a value of less than 112 micrograms per gram of fresh weight because the probability of such an event is 0.1401 which is not unlikely.

Option B